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16 Cards in this Set
- Front
- Back
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Heron
1. Where from? 2. What were his two works called? 3. What did he find out? |
1. an Egyptian with Greek training
2. Geometric (problems on mensuration) and Mechanical (descriptsion of ingenious mechanical devices) 3. A method of finding a sqrt approximation of a nonsquare interger |
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Heron's method of finding square root approximation.
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If n=ab, then sqrt(n) is approximated by (a+b)/2, then the approximation improving with the closeness of a tob.
a(1) = first guess a(2) = [a(1)+n/a(1)]/2 a(3) = [a(2)+n/a(2)]/2 |
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Use Heron's method of sqrt approxmation to find the square root of 54.
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7.35
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What are the three stages in historical development of algebraic notation ?
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1. Rhetorical Algebra
2. Synocopated Algebra 3. Symbolic Algebra |
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Rhetorical Algebra
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Solution of a problem written without abbreviations of symbols
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Syncopated Algebra
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Abbreviations are adopted for some of the more frequrently reoccuring quantities and operations
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Symbolic Algebra
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Solutions appear largely in a mathematical shorthand made up of symbols having little apparent connection with teh entities they represent.
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Three works of Diophantus
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1. Arithmetica
2. On Polygonal Numbers 3. Porisms |
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Diophantine Problems
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Intermediate algebraic problems in which one must find only the rational solutions
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How do you solve a Diophantine Equation?
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a is similar to b (mod m) if and only if a/m, b/m have the same remainder
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What work did Ptolemy Soltec write?
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"Al-majest"
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State Ptolmey's Theorem
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In a cyclic quadrilateral, the product of the diagonals is equal to the sum of the prodcuts of the two pairs of opposite sides
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What is Ptolemy's method of square root?
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Refer to book, pg 177
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What are the two types of Liberal Arts?
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1. Quadrivium
2. Trivium |
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What are the four Quadrivium?
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1. Arithmetic
2. Music 3. Geometry 4. Astronomy |
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What are the Three Trivium?
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1. Logic
2. Grammar 3. Rhetoric |
